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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Atomic-Scale Imaging Reveals Polar-π Interactions in Two-Dimensional Molecular Superlattices

Controlling coassembly of synthetic oligomers into binary superlattices at the atomic level is challenging. Here, we report a strategy for programming polar-π interactions in oligomeric peptoids, a class of sequence-defined peptidomimetics, facilitating the formation of homogeneous two-dimensional (2D) superlattices. N-2-phenylethyl and N-(2-perfluorophenyl)ethyl side chains, similar in size, but with contrasting electrostatic characteristics, were introduced at defined sequence positions to generate favorable dipolar aromatic interactions. The resulting nanosheets exhibit different crystal motifs depending on the side chain interactions: systems containing only one type of aromatic side chain form a parallel V-shaped motif driven by π-π interactions, whereas a combination of both types of aromatic side chains, either within one backbone or through the coassembly of two distinct peptoids, adopt an antiparallel V-shaped superlattice with higher thermal stability, driven by polar-π interactions. Cryogenic transmission electron microscopy directly resolved the packing arrangement of perfluorophenyl and phenyl rings in individual nanosheet superlattices, confirming that intermolecular polar-π interaction dominates the superlattice motifs and increases lattice stability. Molecular dynamics simulations and density functional theory calculations further substantiate the energetic favorability of polar-π interactions over π-π interactions, rationalizing the formation of homogeneous superlattices with enhanced thermal stability. Our discoveries establish a design principle for binary coassembly using sequence-defined oligomers, which enables control over unit cell geometry, lattice stability, and molecular registration through aromatic side chain polarization and sequence control. This ability to program atomic-scale binary superlattices opens new avenues for designing functional 2D soft materials.

Lee, Yen Jea [Lawrence Berkeley National Laborator↗
DOE OSTI2023

Using Metadynamics to Reveal Extractant Conformational Free Energy Landscapes

Understanding the impact of extractant functionalization on metal-binding energetics in liquid-liquid extraction is essential to guide the development of better separation processes. Traditionally, computational extractant design uses electronic structure calculations on metal-ligand clusters to determine the metal-binding energy of the lowest energy state. Although highly accurate, this approach does not account for all of the relevant physics encountered under experimental conditions. Such methodologies often neglect entropic contributions such as temperature effects and ligand flexibility, in addition to approximating solvent-extractant interactions with implicit solvent models. In this study, we use classical molecular dynamics simulations with an advanced sampling method, metadynamics, to map out extractant molecule conformational free energies in the condensed phase. Here we generate the complete conformational landscape in solution for a family of bidentate malonamide-based extractants with different functionalizations of the headgroup and the side chains. In particular, we show how such alkyl functionalization reshapes the free energy landscape, affecting the free energy penalty of organizing the extractant into the cis-like metal-binding conformation from the trans-like conformation of the free extractant in solution. Specifically, functionalizing alkyl tails to the center of the headgroup has a greater influence on increasing molecular rigidity and disfavoring the binding conformation than functionalizing side chains. These findings are consistent with trends in metal-binding energetics based on experimentally reported distribution ratios. We also consider a different bidentate extractant molecule, carbamoylmethylphosphine oxide, and show how the choice of solvent can further reshape the conformational energetic landscape. This study demonstrates the feasibility of using molecular dynamics simulations with advanced sampling techniques to investigate extractant conformational energetics in solution, which, more broadly, will enable extractant design that accounts for entropic effects and explicit solvation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

The Atomic Drill Bit: Precision Controlled Atomic Fabrication of 2D Materials

The ability to deterministically fabricate nanoscale architectures with atomic precision is the central goal of nanotechnology, whereby highly localized changes in the atomic structure can be exploited to control device properties at their fundamental physical limit. Here, an automated, feedback-controlled atomic fabrication method is reported and the formation of 1D–2D heterostructures in MoS 2 is demonstrated through selective transformations along specific crystallographic orientations. The atomic-scale probe of an aberration-corrected scanning transmission electron microscope (STEM) is used, and the shape and symmetry of the scan pathway relative to the sample orientation are controlled. The focused and shaped electron beam is used to reliably create Mo 6 S 6 nanowire (MoS-NW) terminated metallic-semiconductor 1D–2D edge structures within a pristine MoS 2 monolayer with atomic precision. From these results, it is found that a triangular beam path aligned along the zig-zag sulfur terminated (ZZS) direction forms stable MoS-NW edge structures with the highest degree of fidelity without resulting in disordering of the surrounding MoS 2 monolayer. Density functional theory (DFT) calculations and ab initio molecular dynamic simulations (AIMD) are used to calculate the energetic barriers for the most stable atomic edge structures and atomic transformation pathways. These discoveries provide an automated method to improve understanding of atomic-scale transformations while opening a pathway toward more precise atomic-scale engineering of materials.

2D materials↗
DOE OSTI2021

Effect of Helium Flux on Near-surface Helium Accumulation in Plasma-Exposed Tungsten

We report results of object kinetic Monte Carlo (OKMC) simulations aimed at understanding the effect of helium flux on the near-surface helium accumulation in plasma-facing tungsten, which is initially defect-free and has a W(100) surface orientation. These OKMC simulations are performed at 933 K for fluxes ranging from 10 22 to 4 × 10 25 He/m 2 s, with 100 eV helium atoms impinging on a W(100) surface up to a maximum fluence of 4×10 19 He/m 2 . In the near-surface region, helium clusters interact elastically with the free surface. The interaction is attractive and results in the drift of mobile helium clusters towards the surface as well as increased trap mutation rates. The associated kinetics and energetics of the above-mentioned processes obtained from molecular dynamics simulations are also considered. The OKMC simulations indicate that as the flux decreases, the retention of implanted helium decreases, and its depth distribution shifts to deeper below the surface in initially pristine tungsten. Furthermore, the fraction of retained helium diffusing into the bulk increases as well, so much so that for 10 22 He/m 2 s, almost all of the retained helium diffused into the bulk with minimal/negligible near-surface helium accumulation. At a given flux, with increasing fluence, the fraction of retained helium initially decreases and then starts to increase after reaching a minimum. The occurrence of the retention minimum shifts to higher fluences as the flux decreases. Although the near-surface helium accumulation spreads deeper into the material with decreasing flux and increasing fluence, the spread appears to saturate at depths between 80 and 100 nm. Finally, we present a detailed analysis of the influence of helium flux on the size and depth distribution of total helium and helium bubbles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Dislocation loop evolution in Kr-irradiated ThO 2

Here, the early stage of microstructural evolution of ThO 2 , under krypton irradiation at 600, 800, and 1000°C, was investigated using in situ transmission electron microscopy (TEM). Dislocation loops grew faster, whereas their number density decreased with increasing irradiation temperature. Loop density was found to decrease with ion dose. Interstitial dislocation loops, including Frank loops with Burgers vector of $\textit{a}/3\langle111\rangle$ and perfect loops with Burgers vector of $\textit{a}/2\langle110\rangle$, were determined by traditional TEM and atomic resolution–scanning TEM techniques. Atomistic and mesoscale level modeling are performed to interpret experimental observations. The migration energy barriers of defects in ThO 2 were calculated using density-functional theory. The energetics of different dislocation loop types were studied using molecular dynamics simulations. Loop density and diameter were analyzed using a kinetic rate theory model that considers stoichiometric loop evolution. This analysis reveals that loop growth is governed by the mobility of cation interstitials, whereas loop nucleation is determined by the mobility of anion defects. Lastly, a rate theory model was used to extract the diffusion coefficients of thorium interstitials, oxygen interstitials, and vacancies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Advancing Multiscale Simulation of Plasma-Surface Interfaces

We report the development of an atomistic-informed, surface-state-dependent predictive model for particle exchange in a carbon-tungsten plasma-surface interface. The predictive model uses machine learning (ML) techniques to learn the energy and angular distributions for particle exchange and rate functions for surface state evolution from molecular dynamics simulations of cumulative bombardment of tungsten by energetic carbon ions. Each predictive component is sensitive to the energy and trajectory of incident plasma species and the surface state. The surface state is represented by a set of surface state descriptors, which were derived from the atomistic surface state for each independent carbon bombardment event. These descriptors are representative of the composition and degree of amorphization of the outermost angstrom of surface material and were chosen to optimize predictive performance for particle exchange at the interface. The distributions for particle exchange (reflection/sputtering) are demonstrated to vary with each surface state descriptor, motivating the development of surface-state-dependent particle exchange models for plasma simulations. The performance of various ML methods was compared, including polynomial quantile regression, artificial neural networks, k-nearest neighbors, and random forest algorithms, with polynomial regression performing the best for interpolation and extrapolation of learned relationships. In addition to the particle exchange model, a neutral network was developed and used to identify data sufficiency throughout surface descriptor space, which will enable real-time feedback during future data production to ensure data is produced where it is most needed, and we provide commentary on improvements to the data production workflow for future endeavors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Data Mining of Polymer Phase Transitions upon Temperature Changes by Small and Wide-Angle X-ray Scattering Combined with Raman Spectroscopy

The complex physical transformations of polymers upon external thermodynamic changes are related to the molecular length of the polymer and its associated multifaceted energetic balance. The understanding of subtle transitions or multistep phase transformation requires real-time phenomenological studies using a multi-technique approach that covers several length-scales and chemical states. A combination of X-ray scattering techniques with Raman spectroscopy and Differential Scanning Calorimetry was conducted to correlate the structural changes from the conformational chain to the polymer crystal and mesoscale organization. Current research applications and the experimental combination of Raman spectroscopy with simultaneous SAXS/WAXS measurements coupled to a DSC is discussed. In particular, we show that in order to obtain the maximum benefit from simultaneously obtained high-quality data sets from different techniques, one should look beyond traditional analysis techniques and instead apply multivariate analysis. Data mining strategies can be applied to develop methods to control polymer processing in an industrial context. Crystallization studies of a PVDF blend with a fluoroelastomer, known to feature complex phase transitions, were used to validate the combined approach and further analyzed by MVA.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Molecular Dynamics Free Energy Simulations Reveal the Mechanism for the Antiviral Resistance of the M66I HIV-1 Capsid Mutation

While drug resistance mutations can often be attributed to the loss of direct or solvent-mediated protein−ligand interactions in the drug-mutant complex, in this study we show that a resistance mutation for the picomolar HIV-1 capsid (CA)-targeting antiviral (GS-6207) is mainly due to the free energy cost of the drug-induced protein side chain reorganization in the mutant protein. Among several mutations, M66I causes the most suppression of the GS-6207 antiviral activity (up to ~84,000-fold), and only 83- and 68-fold reductions for PF74 and ZW-1261, respectively. To understand the molecular basis of this drug resistance, we conducted molecular dynamics free energy simulations to study the structures, energetics, and conformational free energy landscapes involved in the inhibitors binding at the interface of two CA monomers. To minimize the protein−ligand steric clash, the I66 side chain in the M66I−GS-6207 complex switches to a higher free energy conformation from the one adopted in the apo M66I. In contrast, the binding of GS-6207 to the wild-type CA does not lead to any significant M66 conformational change. Based on an analysis that decomposes the absolute binding free energy into contributions from two receptor conformational states, it appears that it is the free energy cost of side chain reorganization rather than the reduced protein−ligand interaction that is largely responsible for the drug resistance against GS-6207.

Sun, Qinfang (ORCID:0000000173621543)↗
DOE OSTI2024

High pressure suppression of plasticity due to an overabundance of shear embryo formation

Abstract High pressure shear band formation is a critical phenomenon in energetic materials due to its influence on both mechanical strength and mechanochemical activation. While shear banding is known to occur in a variety of these materials, the governing dynamics of the mechanisms are not well defined for molecular crystals. We conduct molecular dynamics simulations of shock wave induced shear band formation in the energetic material 1,3,5-trinitroperhydro-1,3,5-triazine (RDX) to assess shear band nucleation processes. We find, that at high pressures, the initial formation sites for shear bands, “embryos”, form in excess and rapidly lower deviatoric stresses prior to shear band formation and growth. This results in the suppression of plastic deformation. A local cluster analysis is used to quantify and contrast this mechanism with a more typical shear banding seen at lower pressures. These results demonstrate a mechanism that is reversible in nature and that supersedes shear band formation at increased pressures. We anticipate that these results will have a broad impact on the modeling and development of high-strain rate application materials such as those for high explosives and hypersonic systems.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Energetics of polymeric carbon monoxide

The transformation of carbon monoxide (CO) from a molecular liquid to a polymeric solid under isothermal compression at room temperature is investigated using first principles theory. We report structural and thermodynamic properties from ambient density up to 2.45 g/cc obtained using density functional theory molecular dynamics simulations, including hybrid exchange corrections. The theoretical results are compared with newly obtained polymeric CO samples, synthesized in a large volume press. The explosive performance of polymeric CO is predicted and discussed. Under most favorable assumptions, it is found to be comparable to trinitrotoluene.

25 ENERGY STORAGE↗
DOE OSTI2022

Following excited-state chemical shifts in molecular ultrafast x-ray photoelectron spectroscopy

The conversion of photon energy into other energetic forms in molecules is accompanied by charge moving on ultrafast timescales. We directly observe the charge motion at a specific site in an electronically excited molecule using time-resolved x-ray photoelectron spectroscopy (TR-XPS). We extend the concept of static chemical shift from conventional XPS by the excited-state chemical shift (ESCS), which is connected to the charge in the framework of a potential model. This allows us to invert TR-XPS spectra to the dynamic charge at a specific atom. We demonstrate the power of TR-XPS by using sulphur 2p-core-electron-emission probing to study the UV-excited dynamics of 2-thiouracil. The method allows us to discover that a major part of the population relaxes to the molecular ground state within 220–250 fs. In addition, a 250-fs oscillation, visible in the kinetic energy of the TR-XPS, reveals a coherent exchange of population among electronic states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Detonation Waves in High Explosives

A material at high temperature can react or decompose. For an energetic material, the reaction is exothermic and releases chemical energy that would further increase the temperature. Under some circumstances, when a reaction is triggered, such a reaction can propagate and the material rapidly releases a large amount of energy giving rise to an explosion. Examples of such materials are aerosols, suspensions of solid particles or liquid droplets in a gas; such as coal dust, grain dust and fuel-air explosions. Frequently, explosions are due to accidents. A spectacularly destructive example is the recent explosion of a large quantity of ammonium nitrate (thousands of tons) in Beirut, Lebanon (August 2020); see for example Beirut explosion. Ammonium nitrate is used as a fertilizer. It and the aerosols are not considered to be explosives due to the limited conditions for which an explosion can occur. An aerosol gets the oxidizer from the surrounding air. Burning requires diffusion of the oxidizer to the particle surface where the reaction occurs. A large density of small particles is required for a fast enough reaction to support an explosion. In contrast, an explosive is an energetic material with both fuel and oxidizer mixed on a molecular scale (either premixed gases or within molecules of a solid). This allows fast enough reactions over a wide range of conditions to support a self-propagating reactive wave known as a detonation wave. A detonation wave can be controlled and an explosive used for useful purposes such as in mining, construction, demolition, explosive welding, argon flash lamp, pulsed power using a magnetic flux generator [see also Goforth et al., 2015], jet cutter with shaped charge, explosive art, and generating conditions to study the response of materials at high strain rates and high pressures [see for example, Marsh, 1980]. Explosives are also used in conventional munitions and nuclear weapons. The focus of this book is on the theory and phenomenology of solid high explosives (HEs); in particular, plastic-bonded explosives (PBXs). Some aspects of detonation wave theory are needed to interpret explosive data. Hence, the theory is presented before the detonation wave phenomenology. A familiarity with fluid flow, specifically the notion of shock waves and the shock loci are assumed. In the remainder of this chapter we give a brief overview on the basic properties of detonation waves and PBXs.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Characterizing Surface Ice-Philicity Using Molecular Simulations and Enhanced Sampling

The formation of ice, which plays an important role in diverse contexts ranging from cryopreservation to atmospheric science, is often mediated by solid surfaces. Although surfaces that interact favorably with ice (relative to liquid water) can facilitate ice formation by lowering nucleation barriers, the molecular characteristics that confer ice-philicity to a surface are complex and incompletely understood. To address this challenge, here we introduce a robust and computationally efficient method for characterizing surface ice-philicity that combines molecular simulations and enhanced sampling techniques to quantify the free energetic cost of increasing surface–ice contact at the expense of surface–water contact. Using this method to characterize the ice-philicity of a family of model surfaces that are lattice matched with ice but vary in their polarity, we find that the nonpolar surfaces are moderately ice-phobic, whereas the polar surfaces are highly ice-philic. In contrast, for surfaces that display no complementarity to the ice lattice, we find that ice-philicity is independent of surface polarity and that both nonpolar and polar surfaces are moderately ice-phobic. Furthermore, our work thus provides a prescription for quantitatively characterizing surface ice-philicity and sheds light on how ice-philicity is influenced by lattice matching and polarity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Mitigating Damage to Hybrid Perovskites Using Pulsed-Beam TEM

Using a pulsed-beam transmission electron microscope, we discover a reduction in damage to methylammonium lead iodide (MAPbI3) as compared to conventional beams delivered at the same dose rates. For rates as low as 0.001 e·Å –2 ·s –1 , we find up to a 17% reduction in damage at a total dose of 10 e·Å –2 . We systematically study the effects of number of electrons in each pulse and the duration between pulse arrival. Damage increases for both, though the number of electrons per pulse has a larger effect. A crossover is identified, where a pulsed beam causes more damage than a conventional one. Although qualitatively similar to previous findings, the degree to which damage is reduced in MAPbI3 is less than that observed for other materials (e.g., C36H74), supporting the hypothesis that the effects are material- and damage-mechanism-dependent. Despite this, the observation here of damage reduction for relatively large electron packets (up to 200 electrons per pulse) suggests that MAPbI3 is in fact less susceptible to irradiation than C36H74, which may be related to reported self-healing effects. This work provides insights into damage processes and durability in hybrid perovskites and also illustrates the viability of using pulsed-beam TEM to explore the associated molecular-level routes to degradation, analogous to laser-accelerated energetic pulsed electron beams and the study of damage to biomolecules, cells, and tissues in radiobiology.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Revitalizing Iron Redox by Anion-Insertion-Assisted Ferro- and Ferri-Hydroxides Conversion at Low Alkalinity

Iron hydroxides are desirable alkaline battery electrodes for low cost and environmental beneficence. However, hydrogen evolution on charging and Fe 3 O 4 formation on discharging cause low storage capacity and poor cycling life. Here, we report that green rust (GR) (Fe 2+ 4 Fe 3+ 2 (HO – ) 12 SO 4 ), formed via sulfate insertion, promotes Fe(OH) 2 /FeOOH conversion and shows a discharge capacity of ~211 mAh g –1 in half-cells and Coulombic efficiency of 93% after 300 cycles in full-cells. Theoretical calculations show that Fe(OH) 2 /FeOOH conversion is facilitated by intercalated sulfate anions. Classical molecular dynamics simulations reveal that electrolyte alkalinity strongly impacts the energetics of sulfate solvation, and low alkalinity ensures fast transport of sulfate ions. Anion-insertion-assisted Fe(OH) 2 /FeOOH conversion, also achieved with Cl – ion, paves a pathway toward efficient utilization of Fe-based electrodes for sustainable applications.

25 ENERGY STORAGE↗
DOE OSTI2024

Side chain engineering in indacenodithiophene- co -benzothiadiazole and its impact on mixed ionic–electronic transport properties

Organic semiconductors are increasingly being decorated with hydrophilic solubilising chains to create materials that can function as mixed ionic–electronic conductors, which are promising candidates for interfacing biological systems with organic electronics. While numerous organic semiconductors, including p- and n-type materials, small molecules and polymers, have been successfully tailored to encompass mixed conduction properties, common to all these systems is that they have been semicrystalline materials. Here, we explore how side chain engineering in the nano-crystalline indacenodithiophene-co-benzothiadiazole (IDTBT) polymer can be used to instil ionic transport properties and how this in turn influences the electronic transport properties. This allows us to ultimately assess the mixed ionic–electronic transport properties of these new IDTBT polymers using the organic electrochemical transistor as the testing platform. Using a complementary experimental and computational approach, we find that polar IDTBT derivatives can be infiltrated by water and solvated ions, they can be electrochemically doped efficiently in aqueous electrolyte with fast doping kinetics, and upon aqueous swelling there is no deterioration of the close interchain contacts that are vital for efficient charge transport in the IDTBT system. Despite these promising attributes, mixed ionic–electronic charge transport properties are surprisingly poor in all the polar IDTBT derivatives. Albeit a “negative” result, this finding clearly contradicts established side chain engineering rules for mixed ionic–electronic conductors, which motivated our continued investigation of this system. We eventually find this anomalous behaviour to be caused by increasing energetic disorder in the polymers with increasing polar side chain content. We have investigated computationally how the polar side chain motifs contribute to this detrimental energetic inhomogeneity and ultimately use the learnings to propose new molecular design criteria for side chains that can facilitate ion transport without impeding electronic transport.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Revealing hidden defects through stored energy measurements of radiation damage

With full knowledge of a material’s atomistic structure, it is possible to predict any macroscopic property of interest. In practice, this is hindered by limitations of the chosen characterization techniques. For example, electron microscopy is unable to detect the smallest and most numerous defects in irradiated materials. Instead of spatial characterization, we propose to detect and quantify defects through their excess energy. Differential scanning calorimetry of irradiated Ti measures defect densities five times greater than those determined using transmission electron microscopy. Our experiments also reveal two energetically distinct processes where the established annealing model predicts one. Molecular dynamics simulations discover the defects responsible and inform a new mechanism for the recovery of irradiation-induced defects. The combination of annealing experiments and simulations can reveal defects hidden to other characterization techniques and has the potential to uncover new mechanisms behind the evolution of defects in materials.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Th 2 O – , Th 2 Au – , and Th 2 AuO 1,2 – Anions: Photoelectron Spectroscopic and Computational Characterization of Energetics and Bonding

The observation and characterization of the anions: Th 2 O – , Th 2 Au – , and Th 2 AuO 1,2 – is reported. These species were studied through a synergetic combination of anion photoelectron spectroscopy and ab initio correlated molecular orbital theory calculations at the CCSD(T) level with large correlation-consistent basis sets. To better understand the energetics and bonding in these anions and their corresponding neutrals, a range of smaller diatomic to tetratomic species were studied computationally. Correlated molecular orbital theory calculations at the CCSD(T) level showed that in most of these cases, there are close-lying anions and neutral clusters with different geometries and spin states and are consistent with the experimentally observed spectra. Thus, comparison of experimentally determined and computationally predicted vertical detachment energies and electron affinities for different optimized geometries and spin states shows excellent agreement to within 0.1 eV. The structures for both the neutrals and anions have a significant ionic component to the bonding because of the large electron affinity of the Au atom and modest ionization potentials for Th 2 , Th 2 O, and Th 2 O 2 . The analysis of the bonding for the Th–Th bonds from the molecular orbitals is consistent with this ionic model. The results show that there is a wide variation in the bond distance from 2.7 to 3.5 Å for the Th–Th bonds all of which are less than twice the atomic radius of Th of 3.6 Å. The bond distances encompass bond orders from 4 to 0. Furthermore, there can be different bond orders for the same bond distance depending on the nature of the ionic bonding suggesting that one may not be able to correlate the bond order with the bond distance in these types of clusters. In addition, the presence of an Au atom may provide a unique probe of the bonding in such clusters because of its ability to accept an electron from clusters with modest ionization potentials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗